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Some badges can be awarded multiple times.
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MysticialAug 14 '12 at 9:15

Badges are not upgraded, they accumulate. For example, suppose you get the bronze "Nice Question" badge for a question with score 10. If that question achieves a score of 25 later, you will get the silver "Good Question" badge in addition to your "Nice Question" badge.
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S.L. BarthAug 14 '12 at 9:27

From the linked faq: Some badges can be earned more than once. If a user earns such a badge more than once, his name will appear on that badge's page once for each time he earned the badge. The badges listing on the user page will also display a multiplier next to the badge indicating the number of times it has been earned
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Shadow WizardAug 14 '12 at 9:28

As for "Can be the bronze badge be changed to a silver badge, and a silver badge changed to a gold badge?" it is not covered in the faq and the answer is "No" - badge is permanent, you can earn silver badge in addition to bronze one, it's not "upgrading" the bronze.
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Shadow WizardAug 14 '12 at 9:31

@SLBarth then maybe this question will get the bronze "Bad Question"
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Josua Marcel ChrisanoAug 14 '12 at 9:35

@Josua no worry, we were all new. However only badge one can gain for downvoted posts is Peer Pressure when deleting -3 or lower post - not relevant in your case since you can't delete your question now having an answer on it.
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Shadow WizardAug 14 '12 at 9:41